Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13133292 | C2 | semidirect |
| 2. C2×#16811518 | C2 | semidirect |
| 3. C2×#16811518 | C2 | semidirect |
| 4. #20289753 | C2 | semidirect |
| 27. C2×#11719910 | D4 | semidirect |
| 105. C22×D53 | M32 | semidirect |
| 110. C2×C4×C53 | M32 | semidirect |
| 182. C53 | #12977 | semidirect |
| 283. C2×C4 | #13133292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133292 | 2 |
| C2×#16811518 | 2 |
| #20289753 | 2 |
| C2×#16810688 | 2 |
| #12977 | 53 |